.
, :
. (1.28)
, k=2 k>2. , , .
. 1.2.
1.2
X1 | X2 | X3 | X | Y | ||
. . . N | X11 X12 X13 . . . X1N | X21 X22 X23 . . . X2N | X31 X32 X33 . . . X3N | Xk1 Xk2 Xk3 . . . XkN | Y1 Y2 Y3 . . . YN |
, :
; ; , (1.29)
yi0, x1i0, x2i0 ,
- ,
sy, sx1, sx2 .
; ; .
1.3 .
1.3
.. | |||||
. . . N | X011 X012 X013 . . . X01N | X021 X022 X023 . . . X02N | X031 X032 X033 . . . X03N | Y01 Y02 Y03 . . . Y0N |
:
; . (1.30)
(1.31)
:
. (1.32)
(1.32) :
.
S , :
; (1.33)
:
. (1.34)
. , (1.34), r*. , :
(1.35)
, . 1.3.
(1.35), R:
. (1.36)
:
R . , , . :
, (1.37)
R ; l .
(1.32) :
. (1.38)
(. 1.4).
, ( 1.4 2).
|
|
1.4
, / | , / | |||||||
163.5 | 3620.8 | 9654.5 | 14344.8 | 5660.7 | 6261.3 | 1950.6 | 18306.0 | |
90.0 | 3361.4 | 6942.0 | 14195.4 | 4780.0 | 4790.6 | 3758.6 | 19451.0 | |
117.0 | 7593.0 | 6557.0 | 12891.5 | 4455.5 | 3687.5 | 3955.5 | 22301.0 | |
97.4 | 5883.5 | 4235.0 | 12328.5 | 5425.5 | 4202.0 | 6239.5 | 17876.0 | |
59.0 | 2295.0 | 4142.5 | 8360.0 | 4217.5 | 4802.5 | 2637.5 | 11000.0 | |
228.5 | 6592.5 | 8132.5 | 16640.0 | 4010.0 | 3392.5 | 3185.0 | 22400.0 | |
75.5 | 3475.5 | 7815.0 | 15770.0 | 4395.0 | 5100.0 | 8695.0 | 17970.0 |
1.4
, [oC] | , [oC] | , [oC] | , [3/] | , [3/] | ||
Y | ||||||
Y | ||||||
1.4
t , (0) | t , (0) | , (/2) | t, (0) | |
7.9 | ||||
7.9 | ||||
7.7 | ||||
8.5 | ||||
8.5 | ||||
8.0 | ||||
8.0 | ||||
8.0 | ||||
8.0 | ||||
5.6 | ||||
5.6 | ||||
8.0 | ||||
8.0 | ||||
8.0 | ||||
5.1 |
1.4 | ||||||
7,8 | 0,5 | 9,5 | ||||
7,7 | 9,4 | |||||
7,8 | 0,3 | 9,8 | ||||
7,8 | 9,4 | |||||
7,8 | 0,2 | 9,6 | ||||
7,8 | 0,2 | 9,5 | ||||
7,8 | 0,2 | 9,5 | ||||
7,8 | 0,2 | 9,7 | ||||
0,2 | 10,1 | |||||
0,1 | ||||||
8,1 | 0,1 | 9,9 | ||||
7,8 | 0,1 | 9,6 | ||||
7,9 | 0,4 | 9,4 | ||||
7,6 | 0,5 | 9,3 | ||||
7,3 | 0,5 | 9,2 | ||||
7,6 | 0,2 | 9,2 | ||||
7,6 | 0,8 | 9,7 | ||||
7,9 | 0,6 | 9,8 | ||||
0,5 | 9,5 | |||||
0,4 |
|
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1. .
2. .
3. .
4. .
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4
2k.
( 2k). . .
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;
.
:
; (1.39)
. (1.40)
() , ; , . . ():
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+1, -1, . k = 3. N N = 2k = 23 = 8. ( ) 1.5.
, , .
23 , .
1.6 :
; (1.42)
;
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k ; N .
( 1.42) - . , , (*) N. (*)-1.
|
|
.
1.5
23
Z1 | Z2 | Z3 | X1 | X2 | 3 | Y | |
-1 +1 -1 +1 -1 +1 +1 +1 | -1 -1 +1 +1 -1 -1 +1 +1 | -1 -1 -1 -1 +1 +1 +1 +1 |
1.6
N | X0 | X1 | X2 | X3 | Y |
+1 +1 +1 +1 +1 +1 +1 +1 | -1 +1 -1 +1 -1 +1 -1 +1 | -1 -1 +1 +1 -1 -1 +1 +1 | -1 -1 -1 -1 +1 +1 +1 +1 | Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 |
,
. (1.44)
, bj y xj, N:
. (1.45)
, 1.5, :
. (1.46)
, b1 1 :
:
b0 = 18,5 b2 = -0,5 b3 = +3,5
:
. (1.47)
b12, b13, b23 ( ) b123 ( ) ( 1.7) :
1.7
X0 | X1 | X2 | X3 | X12 | X13 | X23 | X123 | Y | |
+1 +1 +1 +1 +1 +1 +1 +1 | -1 +1 -1 +1 -1 +1 -1 +1 | -1 -1 +1 +1 -1 -1 +1 +1 | -1 -1 -1 -1 +1 +1 +1 +1 | +1 -1 -1 +1 +1 -1 -1 +1 | +1 -1 +1 -1 -1 +1 -1 +1 | +1 +1 -1 -1 -1 -1 +1 +1 | -1 +1 +2 -1 +1 -1 -1 +1 |
.
. .
(. 1.8).
1.8
- | , / | , / | , / | , / | |
6477,0 | 6936,0 | 26,40 | 18,0 | 38476547,9 | |
6477,0 | 6936,0 | 10185,0 | 21,0 | 44546006,0 | |
6477,0 | 10151,0 | 2640,0 | 25,0 | 52670991,5 | |
6477,0 | 10151,0 | 10185,0 | 27,0 | 56719158,0 | |
9183,5 | 6936,0 | 2640,0 | 11,0 | 24296811,9 | |
9183,5 | 6936,0 | 10185,0 | 13,0 | 26300916,3 | |
9183,5 | 10151,0 | 2640,0 | 14,5 | 31399481,9 | |
9183,5 | 10151,0 | 10185,0 | 15,5 | 33423869,8 |
. 1.8 2k, .
1. . .
yˆ = b0+b1x1+b2x2+b3x3+b4x4
2. . :
|
|
yˆ = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b12x1x2 + b13x1x3 + b14x1x2 +
+ b23x2x3 + +b24x2x4 + b34x3x4
3. .
4. .
5. .
(1.41), (1.42) . (1.45).
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F (1,2) [ 1], . .
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.
.
1-4 1 :
1. .
2. .
3. Mathcad.
4. Mathcad.
5. .
1
(F-) p = 0.05
f2 | f1 | |||||||||||||
18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.33 | 19.35 | 19.37 | 19.38 | 19.40 | 19.41 | 19.42 | 19.43 | 19.44 | |
10.13 | 9.55 | 9.28 | 9.12 | 9.01 | 8.94 | 8.89 | 8.85 | 8.81 | 8.79 | 8.74 | 8.71 | 8.69 | 8.66 | |
7.71 | 6.94 | 6.59 | 6.39 | 6.26 | 6.16 | 6.09 | 6.04 | 6.00 | 5.96 | 5.91 | 5.87 | 5.84 | 5.80 | |
6.61 | 5.79 | 5.41 | 5.19 | 5.05 | 4.95 | 4.88 | 4.82 | 4.77 | 4.74 | 4.68 | 4.64 | 4.60 | 4.56 | |
5.99 | 5.14 | 4.76 | 4.53 | 4.39 | 4.28 | 4.21 | 4.15 | 4.10 | 4.06 | 4.00 | 3.96 | 3.92 | 3.87 | |
5.59 | 4.74 | 4.35 | 4.12 | 3.97 | 3.87 | 3.79 | 3.73 | 3.68 | 3.64 | 3.57 | 3.53 | 3.49 | 3.44 | |
5.32 | 4.46 | 4.07 | 3.84 | 3.69 | 3.58 | 3.50 | 3.44 | 3.39 | 3.35 | 3.28 | 3.24 | 3.20 | 3.15 | |
5.12 | 4.26 | 3.86 | 3.63 | 3.48 | 3.37 | 3.29 | 3.23 | 3.18 | 3.14 | 3.07 | 3.03 | 2.99 | 2.93 | |
4.96 | 4.10 | 3.71 | 3.48 | 3.33 | 3.22 | 3.14 | 3.07 | 3.02 | 2.98 | 2.91 | 2.86 | 2.83 | 2.77 | |
4.84 | 3.98 | 3.59 | 3.36 | 3.20 | 3.09 | 3.01 | 2.95 | 2.90 | 2.85 | 2.79 | 2.74 | 2.70 | 2.65 | |
4.75 | 3.89 | 3.49 | 3.26 | 3.11 | 3.00 | 2.91 | 2.85 | 2.80 | 2.75 | 2.69 | 2.64 | 2.60 | 2.54 | |
4.67 | 3.81 | 3.41 | 3.18 | 3.03 | 2.92 | 2.83 | 2.77 | 2.71 | 2.67 | 2.60 | 2.55 | 2.51 | 2.46 | |
4.60 | 3.74 | 3.34 | 3.11 | 2.96 | 2.85 | 2.76 | 2.70 | 2.65 | 2.60 | 2.53 | 2.48 | 2.44 | 2.39 | |
4.54 | 3.68 | 3.29 | 3.06 | 2.90 | 2.79 | 2.71 | 2.64 | 2.59 | 2.54 | 2.48 | 2.42 | 2.38 | 2.33 | |
4.49 | 3.63 | 3.24 | 3.01 | 2.85 | 2.74 | 2.66 | 2.59 | 2.54 | 2.49 | 2.42 | 2.37 | 2.33 | 2.28 | |
4.45 | 3.59 | 3.20 | 2.96 | 2.81 | 2.70 | 2.61 | 2.55 | 2.49 | 2.45 | 2.38 | 2.33 | 2.29 | 2.23 | |
4.41 | 3.55 | 3.16 | 2.93 | 2.77 | 2.66 | 2.58 | 2.51 | 2.46 | 2.41 | 2.34 | 2.29 | 2.25 | 2.19 | |
4.38 | 3.52 | 3.13 | 2.90 | 2.74 | 2.63 | 2.54 | 2.48 | 2.42 | 2.38 | 2.31 | 2.26 | 2.21 | 2.15 | |
4.35 | 3.49 | 3.10 | 2.87 | 2.71 | 2.60 | 2.51 | 2.45 | 2.39 | 2.35 | 2.28 | 2.22 | 2.18 | 2.12 | |
4.32 | 3.47 | 3.07 | 2.84 | 2.68 | 2.57 | 2.49 | 2.42 | 2.37 | 2.32 | 2.25 | 2.20 | 2.16 | 2.10 | |
4.30 | 3.44 | 3.05 | 2.82 | 2.66 | 2.55 | 2.46 | 2.40 | 2.34 | 2.30 | 2.23 | 2.17 | 2.13 | 2.07 | |
4.28 | 3.42 | 3.03 | 2.80 | 2.64 | 2.53 | 2.44 | 2.37 | 2.32 | 2.27 | 2.20 | 2.15 | 2.11 | 2.05 | |
4.26 | 3.40 | 3.01 | 2.78 | 2.62 | 2.51 | 2.42 | 2.36 | 2.30 | 2.25 | 2.18 | 2.13 | 2.09 | 2.03 | |
4.24 | 3.39 | 2.99 | 2.76 | 2.60 | 2.49 | 2.40 | 2.34 | 2.28 | 2.24 | 2.16 | 2.11 | 2.07 | 2.01 |
(F-) p = 0.01
f2 | f1 | |||||||||||||
98.50 | 99.00 | 99.17 | 99.25 | 99.30 | 99.33 | 99.36 | 99.37 | 99.39 | 99.40 | 99.42 | 99.43 | 99.44 | 99.45 | |
34.12 | 30.82 | 29.46 | 28.71 | 28.24 | 27.91 | 27.67 | 27.49 | 27.34 | 27.23 | 27.05 | 26.92 | 26.83 | 26.69 | |
21.20 | 18.00 | 16.69 | 15.98 | 15.52 | 15.21 | 14.98 | 14.80 | 14.66 | 14.55 | 14.37 | 14.25 | 14.15 | 14.02 | |
16.26 | 13.27 | 12.06 | 11.39 | 10.97 | 10.67 | 10.46 | 10.29 | 10.16 | 10.05 | 9.89 | 9.77 | 9.68 | 9.55 | |
13.74 | 10.92 | 9.78 | 9.15 | 8.75 | 8.47 | 8.26 | 8.10 | 7.98 | 7.87 | 7.72 | 7.60 | 7.52 | 7.39 | |
12.25 | 9.55 | 8.45 | 7.85 | 7.46 | 7.19 | 7.00 | 6.84 | 6.72 | 7.62 | 6.47 | 6.36 | 6.27 | 6.16 | |
11.26 | 8.65 | 7.59 | 7.01 | 6.63 | 6.37 | 6.18 | 6.03 | 5.91 | 5.81 | 5.67 | 5.56 | 5.48 | 5.36 | |
10.56 | 8.02 | 6.99 | 6.42 | 6.06 | 5.80 | 5.61 | 5.47 | 5.35 | 5.26 | 5.11 | 5.00 | 4.92 | 4.81 | |
10.04 | 7.56 | 6.55 | 5.99 | 5.64 | 5.39 | 5.20 | 5.06 | 4.94 | 4.85 | 4.71 | 4.60 | 4.52 | 4.41 | |
9.65 | 7.21 | 6.22 | 5.67 | 5.32 | 5.07 | 4.89 | 4.74 | 4.68 | 4.54 | 4.40 | 4.29 | 4.21 | 4.10 | |
9.33 | 6.93 | 5.95 | 5.41 | 5.06 | 4.82 | 4.64 | 4.50 | 4.39 | 4.30 | 4.22 | 4.05 | 3.97 | 3.86 | |
9.07 | 6.70 | 5.74 | 5.21 | 4.86 | 4.62 | 4.44 | 4.30 | 4.19 | 4.10 | 3.96 | 3.86 | 3.78 | 3.66 | |
8.86 | 6.51 | 5.56 | 5.04 | 4.70 | 4.46 | 4.28 | 4.14 | 4.03 | 3.94 | 3.80 | 3.70 | 3.62 | 3.51 | |
8.68 | 6.36 | 5.42 | 4.89 | 4.56 | 4.32 | 4.14 | 4.00 | 3.89 | 3.80 | 3.67 | 3.56 | 3.49 | 3.37 | |
8.53 | 6.23 | 5.29 | 4.77 | 4.44 | 4.20 | 4.03 | 3.89 | 3.78 | 3.69 | 3.55 | 3.45 | 3.37 | 3.26 | |
8.40 | 6.11 | 5.18 | 4.67 | 4.34 | 4.10 | 3.93 | 3.79 | 3.68 | 3.59 | 3.46 | 3.35 | 3.27 | 3.16 | |
8.29 | 6.01 | 5.09 | 4.58 | 4.05 | 4.01 | 3.84 | 3.71 | 3.60 | 3.51 | 3.37 | 3.27 | 3.19 | 3.08 | |
8.18 | 5.93 | 5.01 | 4.50 | 4.17 | 3.94 | 3.77 | 3.63 | 3.52 | 3.43 | 3.30 | 3.19 | 3.12 | 3.00 | |
8.10 | 5.85 | 4.94 | 4.43 | 4.10 | 3.87 | 3.70 | 3.56 | 3.46 | 3.37 | 3.23 | 3.13 | 3.05 | 2.94 | |
8.02 | 5.78 | 4.87 | 4.37 | 4.04 | 3.81 | 3.64 | 3.51 | 3.40 | 3.31 | 3.17 | 3.07 | 2.99 | 2.88 | |
7.95 | 5.72 | 4.82 | 4.81 | 3.99 | 3.76 | 3.59 | 3.45 | 3.35 | 3.26 | 3.12 | 3.02 | 2.94 | 2.83 | |
7.88 | 5.66 | 4.76 | 4.26 | 3.94 | 3.71 | 3.54 | 3.41 | 3.30 | 3.21 | 3.07 | 2.97 | 2.89 | 2.78 | |
7.82 | 5.61 | 4.72 | 4.22 | 3.90 | 3.67 | 3.50 | 3.36 | 3.26 | 3.17 | 3.03 | 2.93 | 2.85 | 2.74 | |
7.77 | 5.57 | 4.68 | 4.18 | 3.86 | 3.63 | 3.46 | 3.32 | 3.22 | 3.13 | 2.99 | 2.89 | 2.81 | 2.70 |
|
|